83.22.18 problem 18

Internal problem ID [19201]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (E) at page 63
Problem number : 18
Date solved : Monday, March 31, 2025 at 06:55:58 PM
CAS classification : [[_homogeneous, `class G`], _rational, _dAlembert]

\begin{align*} 2 y&=x y^{\prime }+\frac {a}{y^{\prime }} \end{align*}

✓ Maple. Time used: 0.040 (sec). Leaf size: 788

ode:=2*y(x) = x*diff(y(x),x)+a/diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 60.158 (sec). Leaf size: 1553

ode=2*y[x]==x*D[y[x],x]+a/D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-a/Derivative(y(x), x) - x*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out